Clocks(Part 4)

Clocks (cont.)
Escapements

The escapement is that part of the clock in which the rotary motion of the wheels is converted into the vibratory motion of the balance or pendulum, which by some contrivance or other is made to let one tooth of the quickest wheel in the train escape at each vibration; and hence that wheel is called the "scape-wheel." Fig. 3 shows the form of the earliest clock escapement, if it is held sideways, so that the arms on which the two balls are set may vibrate on a horizontal plane. In that case the arms and weights form a balance, and the farther out the weights are set, the slower would be the vibrations. If we now turn it as it stands here, and consider the upper weight left out, it becomes the earliest form of the pendulum clock, with the crown-wheel or vertical escapement. CA and CB are two flat pieces of steel, called pallets, projecting from the axis about at right angles to each other, one of them over the front of the wheel as it stands, and the other over the back. The tooth D is just escaping from the front pallet Ca, and at the same time the tooth at the back of the wheel falls on the others pallet CB, a little above its edge. But the pendulum which is now moving to the right does not stop immediately, but swings a little further (otherwise the least failure in the force of the train would stop the clock, as the escape would not take place), and in so doing it is evident that the pallet B will drive the wheel back a little, and produce what is called the recoil; which is visible enough in any common clock with a seconds-hand, either with this escapement or the one which will be next described.

It will be seen, on looking at figure 3, that the pallet B must turn through a considerable angle before the tooth can escape; in other words, the crown-wheel escapement requires a long vibration of the pendulum. This is objectionable on several accounts,first, because it requires a great force in the clock train, and a great pressure, and therefore friction, on the pallets; and besides that, any variation in a large arc, as was explained before, produce a much greater variation of time due to the circular error than an equal variation of a small arc. The crown-wheel escapement may indeed be made so as to allow a more moderate arc of the pendulum, though not so small as the 2º usually adopted in the best clocks, by putting the pallet arbor a good deal higher above the scape-wheel, and giving a small number of teeth to the wheel; and that also diminishes the length of the run of the teeth, and consequently the friction, on the pallets, though it makes the recoil very great and sudden; but, oddly enough, it never appears to have been resorted to until long after the escapement had become superseded by the "anchor" escapement, which we shall new describe, and which appears to have been invented by the celebrated Dr Hooke as early as the year 1656, very soon after the invention of pendulums.

In fig. 4, a tooth of the scape-wheel is just escaping form the left pallet, and another tooth at the same time falls upon the right hand pallet at some distance from its point. As the pendulum moves on in the same direction, the tooth slides farther up the pallet, thus producing a recoil, as in the crown-wheel escapement. The acting faces of the pallets should be convex, and not flat, as they are generally made, much less concave, as they have sometimes been made, with a view of checking the motion of the pendulum, which is more likely to injure the rate of the clock than to improve it. But when they are flat, and of course still more when they are concave, the points of the teeth always wear a hole in the pallets at the extremity of their usual swing, and the motion is obviously easier and therefore better when the pallets are made convex; in fact they then approach more nearly to the "dead" escapement, which will be described presently. We have already alluded to the effect of some escapements I not only counteracting the circular error, or the natural increase of the time of a pendulum as the arc increases, but overbalancing it by an error of the contrary kind. The recoil escapement does so; for it is almost invariably found that whatever may be the shape of these pallets, the clock loses as the arc of the pendulum falls off, and vice versa. It is unfortunately impossible so to arrange the pallets that the circular error may be thus exactly neutralized, because the escapement error depends, in a manner reducible to no law, upon variations in friction of the pallets themselves and of the clock train, which produce different effects; and the result is that it is impossible to obtain very accurate time-keeping from any clock of this construction.

But before we pass on the dead escapement, it may be proper to notice an escapement of the recoiling class, which was invented for the purpose of doing without oil, by the famous Harrison, who was at first a carpenter In Lincolnshire, but afterwards obtained the first Government reward for the improvement of chronometers. We shall not however stop to describe it, since it never came into general use, and it is said that nobody but Harrison himself could make it go at all. It was also objectionable on account of its being directly affected by all variations in the force of the clock. It had the peculiarity of being very nearly silent, though the recoil was very great. Those who are curious about such things will find it described in the seventh edition of this Encyclopedia. The recorded performance of one these clocks, which is given in some accounts of it, is evidently fabulous.

Dead Escapements

The escapement which has now for a century and a half been considered the bets practical clock escapement (though there have been constant attempts to invent one free from the defects which it must be admitted to possess) is the dead escapement, or, as the French call it with equal expressiveness, léchappement à reposbecause instead of the recoil of the tooth upon the pallet, which took place in the previous escapements, it falls dead upon the pallet, and reposes there until the pendulum returns and lets it off again. It is represented in fig. 5. It will be observed that the teeth of the scape-wheel have their points set the opposite way to those of the recoil escapement in fig. 4, the wheels themselves both turning the same way; or (as our engraver has represented it), vice versa. The tooth B is here also represented in the act of dropping on to the right hand pallet as the tooth A escapes from the left pallet. But instead of the pallet having a continuous face as in the recoil escapement, it is divided into two, of which BE on the right pallet, and FA on the left, are called the impulse fates, and BD, FG, the dead faces. The dead faces are portions of circles (nor necessarily of the same circle), having the axis of the pallets C for their centre; and the consequence evidently is, that as the pendulum goes, on, carrying the pallet still never to the wheel than the position in which a tooth balls on the corner A or B of the impulse and the dead faces, the tooth still rests on the dead faces without any recoil, until the pendulum returns and lets the tooth aside down the impulse face, giving the impulse to the pendulum as it goes.

The great merit of this escapement is that a moderate variation in the force of the clock train produces a very slight effect in the time of the pendulum. This may be shown in general way, without resorting to mathematics, thusSince the tooth B drops on to the corner of the pailet (or ought to do so) immediately after the tooth A has escaped, and since the impulse will begin at B when the pendulum returns to the same point at which the impulse ceased on A, it follows that the impulse received by the pendulum before and after its vertical position is very nearly the same. Now that part of the impulse which takes place before zero, or while the pendulum is descending, tends to augment the natural force of gravity on the pendulum, or to make it more faster; but in the descending arc the impulse on the pallets acts against the gravity of the pendulum and prevents it from being stopped so soon; and so the two parts of the impulse tend to neutralize each others disturbing effects on the times of the pendulum, though they both concur in increasing the arc, or (what is the same thing) maintaining it against the loss from friction and resistance of the air. However, on the whole, the effect of the impulse is to retard the pendulum a little, because the tooth must fall, not exactly on the corner of the pallet, but (for safely) a little above it; and the next impulse does not begin until that same corner of the pallet has come as far as the point of the tooth; in other words, the retarding part of the impulse, or that which takes place after zero, acts rather longer than the accelerating part before zero. Again, the friction on the dead part of the pallets tends to produce the same effect on the time; the arc of course it tends to diminish. For in the decent of the pendulum the friction acts against gravity, but in the ascent with gravity, and so shorten the time; and there is rather less action on the dead part of the pallets in the ascent than in the descent. For these reasons, the time of vibration of a pendulum driven by a dead escapement is a little greater than of the same pendulum vibrating the same arc freely; and when you come to the next difference, the variation of time of the same pendulum with the dead escapement, under a moderate variation in the force, is very small indeed, which is not the case in the recoil escapement, for there the impulse begins at each of the arc, and there is much more of it during the descent of the pendulum than during the ascent from zero to the arc at which the escape takes place and the recoil begins on the opposite tooth; and then the recoil itself acts on the pendulum in its ascent in the same direction as gravity, and so shortens the time. And hence it is that an increase of the arc of the pendulum with a recoil escapement is always accompanied with a decrease of the time. Something more than this general reasoning is requisite in order to compare the real value of the dead escapement with others of equal or higher pretensions, or of the several contrivances that have been suggested for remedying its defects. But we must refer to the Rudimentary Treatise on Clocks for details of the mathematical calculations by which the numerical results are obtained, and the relative value of the different kinds of escapement determined.

It cannot be determined a priori whether cleaning and oiling a dead escapement clock will accelerate or retard it, for reasons explained in those calculations; but it may be said conclusively that the larger the arc is for any given weight x the fall per day, the better the clock will be; and in order to diminish the friction and the necessity for using oil as far as possible, the best clocks are made with jewels (sapphires are the best for the purpose) let into the pallets.

The pallets are generally made to embrace about one-third of the circumference of the wheel, and it is not at desirable that they should embrace more; for the longer they are, the longer is the run of the teeth upon them, and the greater the friction. There is a good deal of difference in the practice of clockmakers as to the length of the impulse, or the amount of the angle _ + ß if the impulse begins at ß before zero and at _ after zero. Sometimes you see clocks in which the seconds hand moves very slowly and rests a very short time, showing that _ + ß is large in proportion to 2a; and in other s the contrary. The late Mr Dent was decided of opinion that an short impulse was the best, probably because there is less of the force of the impulse wasted in friction then. It is not to be forgotten that the scape-wheel tooth does not overtake the face of the pallet immediately, on account of the moment of inertia of the wheel. The wheels of astronomical clocks, and indeed of all English house-clocks, are generally made too heavy, especially the scape-wheel, which, by increasing the moment of inertia, requires a larger force, and consequently has more friction. We shall see presently, from another escapement, how much of the force is really wasted in friction in the dead escapement.

But before proceeding to other escapements, it is proper to notice a very useful form of the dead escapement, which is adopted in many of the best turret clocks, called the pin-wheel escapement. Fig. 6 will sufficiently explain its action and construction. Its advantages are-that it does not require so much accuracy as the other; if a pin gets broken it is easily replaced, whereas in the other the wheel is ruined if the point of a tooth is injured; a wheel of given size will work with more pins than teeth, and therefore a train of less velocity will do, and that sometimes amounts to a saving of one wheel in the train, and a good deal of friction; and the blow on both pallets being downwards, instead of one up and the other down, the action is more steady; and which things are of more consequence in the heavy and rough work of a turret clock than in an astronomical one. The details of the construction are given in the Rudimentary Treatise. It has been found expedient to make the dead faces not quite dead, but with a very slight recoil, which rather tends to check the variations of arc, and also the general disposition to lose time if the arc is increased; when so made the escapement is generally called "half-dead."

Passing by the various other modifications of the dead escapement which have been suggested and tried with little or no success, we proceed to describe one of an entirely different form, which was patented in 1851 by Mr C. Macdowall, though it appeared afterwards that one very similar had been tried before, but failed from the proportions being badly arranged. It is represented in fig. 7. The scape-wheel is only a small disc with a single pin in it, made of ruby, parallel and very near to the arbor. The disc turns half round at every beat of the pendulum, and the pin gives the impulse on the vertical faces of the pallets, and the dead friction takes place on the horizontal faces. Its advantages arethat the greatest part of the impulse is given directly across the line of centres, and consequently with very little friction; and therefore also, the friction on the dead faces is less than usual, and scarcely any oil is required; moreover, it is very east to make. But there must be two more wheels in the train, consuming a good deal of the force of the clock-weight by their friction, which rather more than makes up for the friction, which rather more than makes up for the friction saved in the escapement. It was applied successfully to watches, but the expense of the additional wheels prevented their adoption. In order to make the angle of escape not more than 1º, the distance of the pin from the centre of the disc must not be more than 1/60th of the distance of centres of the disc and pallets.

With the view of getting rid of one of these extra wheels in the train, and that pat of the impulse which is least-effective and most oblique, Mr Denison shortly afterwards invented the three-legend dead escapement; which, though afterwards superseded by his three-legged gravity escapement, is still worth notice on account of the exceedingly small force which it requires, thereby giving a practical proof of the large proportion of the force which is wasted in friction in all the other impulse escapements.

In fig. 8, the three long teeth of the scape-wheel are only used for locking on the dead pallets D and E, which are set on the front of the pallets plate; A and B are impulse pallets, being hard bits of steel or jewels set in the pallet plate, and they are acted upon by the three sharp-edges pins which are set in the scape-wheel and point backwards. As soon as the pendulum moves a little further to the left than is here shown the long tooth will slip past the dead pallet or stop D, and the pin at B will run after and catch the corner of that impulse pallet and drive it until the wheel has turned through 60º, and then it will escape; and by that time the uppermost tooth will arrive at the stop E, and will slide along it as in the common dead escapement, but with a pressure as much less than that which gives the impulse as the points of the teeth are farther from the centre of the wheel than the impulse pins are. But the impulse is here given with a little friction, that even where the points of the teeth were made identical with the pins, the clock-weight required to keep the same pendulum with the same train (a common turret-clock movement), swinging to 2º, was only one-fifth of what had been required with the pin-wheel escapement; and the scape-wheel which kept the 6 cwt. Pendulum of the Westminster clock going for half-year, until superseded by the gravity escapement, weighed only a sixth of an ounce. It appears also that it would be possible so to adjust the recoil of the half-dead pallets that the time would not be affected by any small variation of the force and the arc; since it was found that, when a certain amount of recoil was given, the clock gained instead of losing, under an increase of arch due to an increase of clock weight. And if the force were kept constant by a train remontoire, such as will be described hereafter, there would in fact be nothing capable of altering the arc or the time. But on account of the small depth of intersection of the circles of the pins and the pallets, on which its action depends, this escapement requires very careful adjustment of the pallets, except where they are on a large scale; and considering the superior qualities of the corresponding gravity escapement, it is not likely to be used, except perhaps in clocks required to go a long time, in which economy of force is a matter of consequence. The pallets should be connected with the pendulum by a spring fork (which indeed is advisable in the common dead escapement with a heavy pendulum, especially the pin-wheel escapement), to prevent the risk of their driving backwards against the scape-wheel when it is not in motion, as it will not clear itself. The distance of the centres should be not less than 25 times the radius of the circle of the edges of the impulse pins.

Detached Escapements

In all the escapements is hitherto described the pallets are never out of moving contact with the escape-wheel, and there have been several contrivances for keeping them detached except during the impulse and at the moment of passing a click which is to release the wheel to give the impulse. This is an imitation of the chronometer escapement in watches which is sometimes called the "detached." There are only two of such contrivances which appears worth special notice. One was proposed by Sir G. Airy in vol. ii. of the Cambrigde Transactions, but not executed (so far as we know) till a few years ago in the standard sidereal clock at Greenwich, which is reported to go extremely well. Suppose a dead escapement consisting of a single pallets only, say the right hand one of the pin-wheel escapement (fig. 6), for the Greenwich clock has a pin escapement, and that the wheel is locked generally by a spring detent hooking into any one of its teeth, and capable of being lifted or pushed aside by the pendulum, i.e., by a pin somewhere on the single pallet as it passes to the right, but also capable of being passed without being lifted as the pendulum goes to the left. We shall see afterwards how this is done, in the article WATCHES. Then as the pendulum goes to the right, it first lifts the detent at about 1º before zero, and then a tooth or a pin drops on the pallet and gives the impulse, exactly as in the dead pin-wheel escapement and with exactly the same amount of friction, substituting only for the dead friction the resistance and friction of passing the detent one way and lifting it the other.

A different escapement on the same principal bit involving less friction was adopted by Sir E. Beckett in a clock described in the later editions of his book as having gone for above ten years very satisfactorily, except that like all direct im pulse escapements, including Sir G. Airys, it must vary with the force of the clock train, due to different states of the oil. The scape-wheel (fig. 9) is five-legged, and has five sharp-edged pins which give the impulse to the hard steel pallet P whenever it passes to the right, provided the wheel is then free to move. It is stopped by the detent DEF, which turns on a pivot F, not in the pendulum crutch, as it looks in the drawing, but on the clock-frame. When the pendulum going to the right arrives at the position here drawn, the click CE on the crutch pushes the detent aside and so unlocks the wheel, which then gives the impulse, moving through 72º until another tooth arrives at the detent and is stopped, the click having then got far beyond it. When the pendulum returns the click lightly trips over the top of the detent. Here there is practically no friction in giving the impulse, as it is directly across the line of centres, as in the three-legged dead escapement, and the friction of passing and unlocking is as little as possible, for the pressure on the locking teeth is less than half of that of the impulse pins.

In practice the pallet P is a separate but of steel, screwed on, and therefore adjustable. The locking teeth are about 6 inches long from the centre, and the impulse pin-edges _ in. from the centre, which is 7 in. below the top of the pendulum and crutch, so that the impulse begins 1º before zero and ends 1ºafter, corresponding each to 36º turn of the scape-wheel. If r is the distance of the pins from the centre and p the length of the crutch down to the centre, r sin. 36º must=p sin. 1º, if you want an impulse of 1º on each side of O; which makes p=33·7r. BB are eccentric beat pins for adjusting the beat to whatever position of the pendulum you please, i.e., you can make it less than 1º before or after zero as you please. In some respects it would be better to have no crutch, but it would be very difficult to make the adjustments. This escapement should evidently be at the bottom of the clock-frame instead of the top, as in the gravity escapements which will be described presently. The back part of the scape-wheel is carried by a long cock or bridge within which the crutch also moves.

Remontoire or Gravity Escapements

A remontoire escapement is one in which the pendulum does not receive its impulse from the scape-wheel, but from some small weight or spring which is lifted or would up by the scape-wheel at every beat, and the pendulum has nothing to do with the scape-wheel except unlocking it. When this impulse is received from a weight the escapement is also called a gravity escapement, and inasmuch as all the remontoire clock escapements that are worth notice have been gravity escapements, we may use that term for them at once. The importance of getting the impulse given to the pendulum in this way was recognized long before all the properties of the dead escapement, as above investigated, were known. For it was soon discovered that, however superior to the old recoil escapement, it was far from perfect, and that its success depended on reducing the friction of the train and the pallets as far as possible, which involves the necessity of high-numbered pinions and wheels, small pivots, jeweled, pallets, and a generally expensive style of workmanship. Accordingly the invention of an escapement which will give a constant impulse to the pendulum, and be nearly free from friction, has been for a century the great problem of clock-making. We can do no more than shortly notice a very few of the attempts which have been made to solve it. The most simple form of gravity escapement, and the one which will serve the best for investigating their mathematical properties though it fails in some essential mechanical conditions), is that invented by Mudge. The tooth A of the scape-wheel in fig. 10 is resting against the stop or detent a at the end of the pallet CA, from the axis or arbor of which descends the half fork CP to touch the pendulum. From the other pallet CB descends the other half fork CO. The two arbors are set as near the point of suspension, or top of the pendulum spring, as possible. The pendulum, as here represented, must be moving to the right, and just leaving contact with the left pallet and going to take up the right one; as soon as it has raised that pallet a little it will evidently unlock the wheel and let it turn, and then the tooth B will raise the left pallet until it is caught by the stop b on that pallets, and then it will stay until the pendulum returns and releases it by raising that pallet still higher. Each pallet therefore descends with the pendulum to a lower point than that where it is taken up, and the difference between them is supplied by the lifting of each pallet by the clock, which does not act on the pendulum at all; so that the pendulum is independent of all variations of force and friction in the train.

Again referring to the Rudimentary Treatise on Clocks for the mathematical investigation of the errors of this class of escapements, or to a paper by the late J.M. Bloxam, in the R.A.S. Memoirs of 1853, we may say it is proved that though the time of a gravity escapement pendulum differs from that of a free pendulum more than from that of a dead escapement, yet the variations of that difference (which are the real variations of the clock) may be made much less than in any kind of dead escapement.

The difficulty which long prevented the success of gravity escapements was their liability to what is called tripping, Referring again to fig. 10, it will be seen at once that if the scape-wheel should happen to move too fast when it is released, the left pallet will not be raised gradually by the tooth B, but be thrown up with a jerk, perhaps so high that the tooth slips past the hook; and then not only will that tooth slip, but several more, and at last when the wheel is stopped it will be running fast, and the points of some of the teeth will probably be bent of broken by catching against the pallets. And even if the pallet is not raised high enough for the tooth to get past or completely trip, it may still be raised so high that the point of the tooth does not rest on the hook exactly where the slope of the pallet ends, but lower, and the friction between them is quite enough to keep the pallet there; and consequently the pendulum does not begin to lift it at the proper angle _, but at some large angle; and as the pallet always descends with the pendulum to the same point, the duration of the impulse is increased and the pendulum made to spring farther. Sir. E. Beckett called this approximate tripping, and though not so injurious to the clock as actual tripping, it is obviously fatal to its accurate performance, though it appears never to have been noticed before the pointed it out in 1851. Various contrivances have been resorted to for preventing tripping. But on account of the delicacy required in all of them, and other objections, none of them ever came into use until the invention of the three-legged and four-legged escapements to be mentioned presently. The only one which approached near enough to satisfying all the requisite conditions to be worth description is Mr Bloxams, and we accordingly give a sketch of it in fig. 11, which is copied (with a little alteration for distinctness) from his own description of it, communicated in 1853 to the Astronomical Society, some years after he had had it in action in a clock of his own. This drawing will enable any one conversant with these matters to understand its action. He made the pallet arbors cranked, to embrace the pendulum-spring, so that their centres of motion might coincide with that of the pendulum as nearly as possible,perhaps an unnecessary refinement; at least the three-legged and four-legged gravity escapements answer very well with the pallet arbors set on each side of the top of the spring. The size of the wheel determines the length of the pallets, as they must be at such an angle to each other that the radii of the wheel when in contact with each stop may be at right angles to the pallet arm; and therefore, for a wheel of this size, the depth of locking can only be very small. The pinion in Mr Bloxams clock only raised the pallet through 40' at each beat; i.e., the angle which we called _ is only 20º; and probably, if it where increased to anything like a/&Mac195;2, the escapement would trip immediately. The two broad pins marked E,F, are the fork-pins. The clock which Mr Bloxam had went very well; but it had an extremely fine train, with pinions of 18; and nobody else appears to have been able to make one to answer. In short Bloxams was not a practical solution of the gravity escapement problem, any more than those of Captain Kater, or Hardy, or various other inventors. A few clocks of Hardys alone still exist.

The only gravity escapement or escapements that really have come into common use are the "four-legged" and the "double three-legged" escapements of Sir E. Beckett. They passed through various phrases before setting into the present form, of which it is unnecessary to say more than that the first was the single three-legs described in the last edition of this Encyclopaedia, which was suggested by his three-legged dead escapement. A five-legged one was also tried; but though it has some slight advantages they are quite overbalanced by disadvantages, and it requires much more delicacy or construction than either the double three-legs or the four-legs which we shall now describe, remarking that the latter is the best for "regulators," and the former in large clocks. Fig. 22 is a back view of the escapement part of an astronomical clock with the four-legged wheel; seen from the front the wheel would turn the other way. The long locking teeth are made about 2 inches long from the centre, and the lifting pins, of which there are four pointing forwards and the other four intermediate pointing backwards, are at not more than one-30th of the distance between the centres EC, of the wheel and pallets; or rather C is the top of the pendulum spring to which the pallets CS, CS converge, though their actual action are a little below C. It is not worth while to crank them as Mr Bloxam did, in order to make them coincide exactly with the top of the pendulum, as the friction of the beat pins on the pendulum at P is insignificant, and even then would not be quite destroyed. The pallets are not in the same plane, but one is behind and the other in front of the wheel, with one stop pointing backwards and the other forwards to receive the teeth alternatively,it does not matter which; in this figure the stop S is behind and the stop S forward. The pendulum is now going to the right, and just beginning to lift the right pallet and free the stop S; then the wheel will begin to turn and lift the other pallet by one of the pins which is now lowest, and which moves through 45º across the line of centres, and therefore lifts with very little friction. It goes on till the tooth now below S reaches S and is stopped there. Meanwhile the pallet CS goes on with the pendulum as far it may go, to the end of the arc which we have throughout called a, starting from _; but it falls with the pendulum again, not only to _ but to _ on the other side of 0, so that the impulse is due to the weight of each pallet alternatively falling through 2_; and the magnitude of the impulse also depends on the obliqueness of the pallet on the whole, i.e., on the distance of its centre of gravity from the vertical through C. The defect of the original three-legged escapement was that the pallets were too nearly vertical.

Another most material element of these escapements with very few teeth is that they admit of a fly KK on the scape-wheel arbor to moderate its moderate its velocity, which both obviates all risk of tripping, wholly or partially, and also prevents the bang which goes all through the clock where there is not fly. The fly is set on with a friction spring like the common striking-part fly, and should e as long as there is room for, length being much more effective than width. For this purpose the second wheel arbor is shortened and set in a cock fixed on the front plate of the clock, which leaves room for a fly with vanes 2 inches long. The back pivot of the scape-wheel is carried by a long cock behind the back plate, so that the escapement is entirely behind it, close to the pendulum. The pallet arbors are short, as they come just behind the centre wheel, which is here also necessarily above the escapements, and the great wheel arbor on a level with it, and att he left hand (from the front) or the string would be in the 3way of the Fly. No beat screws are required, as the pallets end in mere wires which are easily bent. In is found better to make the tails of the pallets long, rather than short as Mr Bloxam did. It is essential, too, that the angle CSE formed by the tooth and the pallet which is struck upwards should not the least fall short of a right angle, nor the other angle CSE be the least obtuse, or the escapement may very little trip. Practically, therefore, it is safer to let CSE be just greater than 90º and CSE a little less, so that there may not be the least tendency in the blow on the stops to drive the pallets outwards. For the purpose of calculation, however, we must make them both 90º and then it follows that, calling the length of the teeth r, and the distance of centres d, and the length of the pallets from C down to the stops p, r must=d sin. 22 _ and p=d cos. 22 1/2º. Therefore if r is made 2 inches CE or d will be 5·22, say 5 _ inches, and p=4·82. The distance of the lifting pins from the centre will be _ of an inch to make the angle _=1º. It is certainly not desirable to make it more, and even that requires such light pallets for a pendulum of 30 or 40 _, that _ inch distance form the centre is more convenient as giving the smaller lift, assuming the scape-wheel to be from 2 to 2 _ inches in diameter.

Gravity escapements require more weight than a direct impulse escapement with an equally fine train; and they try the accuracy of the wheelcutting more severely. If there is a weak place in the train of a common clock the scape-wheel only follows the pendulum more weekly; but in a gravity escapement it always has to raise the pallets, and ought to raise them quickly, and especially in clocks for astronomical purposes where you take its exact time from the sound of the beats, and so the lifting must not lad and sound uneven. Therefore although a fine train of high numbers is not requisite it must be perfectly well cut. And as the force of the weight does not reach the pendulum its increase is of no consequence, within reasonable limits. It is worth while to put large friction wheels under the arbor of the great wheel in all astronomical clocks, and it makes a material difference in the friction on account of the necessary thickness of the winding arbor. A variation of arc in dead escapement clock is sometimes visible between the beginning and the end of the week according as the string is nearest to the thick or the thin end of the great arbor, when there are no friction wheels.

The other form of the gravity escapement, which is now adopted for large clocks by all the best makers, having been first used in the great Westminster clock, is the double three-legged which is shown in fig. 13. The principle of it is the same as of the four-legs; but instead of the pallets being one behind and the other in front of the wheel, with two sets of lifting pins, there are two sets of lifting pins, there are two wheels ABC, abc, with the three lifting pins and the two pallets between them like a lantern pinion. One step B points forward and the other A backward. The two wheels have their teeth set intermediately or 60º apart, though that is not essential, and the angle of 120º may be divided between them in any other proportions, as 70º and 50º, and in that way the pallets may be still more oblique than 30º from the vertical, which forever is found enough to prevent tripping even if the fly gets loose, which is more likely to happen form carelessness in large clocks than in astronomical ones. The West-minister one was once found to have been left with the spring loose for several days and it had not gained a second, and therefore had never tripped. The two wheels must be both squared on the arbor, or on a collar common to them both, and must not depend upon the three pins or they will shake loose. If the wheels are set with the teeth equidistant, their centre is evidently twice the length of the teeth below C, the theoretical centre of the pallets. The pins should not be farther from the centre than one-24th of the radius of the wheel; and they should be sp placed that the one which is going to lift next may be vertically over the one which has just lifted, and is then holding the other pallet. The third will then be level with the centre; i.e., they will stand on the radii which form the acting faces of the teeth of one of the wheels, and half way between those of the other.

Of course the fly for those escapements in large clocks, with weights heavy enough to drive the hands in all weather, must be mush larger than in small ones. For average church clocks with 1 _ sec. pendulum the legs of the scape-wheels are generally made 4 inches long and the fly from 6 to 7 inches long in each vane by 1 _ or 1 _ wide. For 1 _ sec. pendulums the scape-wheels are generally made 4 _ radius. At Westminster they are 6 inches.

Sir E. Beckett has come to the conclusion that these escapements act better, especially in regulators, if the pallets do not fall quite on the lifting pins, but on a banking, or stops at any convenient place, so as to leave the wheel free at the moment of starting; just as the striking of a common house clock will sometimes fail to start unless the wheel with the pins has a little run before a pin begins to lift the hammer. The best way to manage the banking is to make the beat-pins long enough to reach little way behind the pendulum, and let the banking to a thin plate of any metal screwed adjustably to the back of the case. This plate cannot well shown in the drawings together with the pendulum, which, it may be added, should take up one pallet just when it leaves the other.

It is no longer doubtful that these two escapements are far the best of all for large clocks, the three-legs for very large ones, while the four-legs does very well for smaller turret clocks. And they cost no more to make, though rather more in charged for them by some makers under the pretence than they do. It is absolutely impossible for any large clock exposed to the variations of weather and dust to keep as good time as an ordinary good house clock unless it has either of gravity escapement, or a train remonstoire, which last it much more expensive, to interrupt the variations of force before they reach the pendulum. And though a detached escapement clock while kept clean and the oil in good condition is as good as a gravity one and perhaps better, the gravity one is less affected by variations of the oil, and its rate is altogether more constant. They seem also to have a smaller barometric error.